SOLUTION: Roy is three years older than his sister Mary. In 7 years she will be six-sevenths of his age. How old are they? :))

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Question 511656: Roy is three years older than his sister Mary. In 7 years she will be six-sevenths of his age. How old are they?
:))
Answer by Maths68(1474) About Me  (Show Source):
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Roy is three years older than his sister Mary. In 7 years she will be six-sevenths of his age. How old are they?
Let
Present age of Roy = r
Present age of Mary = m
Roy is three years older than his sister Mary means if we add 3 years to present age of Mary both Roy and Mary will be of equal age
r=m+3...........(1)
In 7 years means we have add 7 in their present age
r+7=m+7
then she will be six-sevenths of his age
6/7(r+7)=(m+7)
6(r+7)=7(m+7)
6r+42=7m+49
6r=7m+49-42
6r-7m=7
Put the value of r from (1) to above equation
6(m+3)-7m=7
6m+18-7m=7
-m=7-18
-m=-11
Multiply by (-1) both sides
m=11
Put the valuel of m in (1)
r=m+3...........(1)
r=11+3
r=14
Present age of Roy = r = 14
Present age of Mary = m = 11

Check
In 7 years Mary will be 6/7 of Roy
Mary=11+7=18
Roy=14+7=21
Mary=6/7(Roy)
Mary=6/7(21)
Mary=6(3)
Mary=18